General eigenstates of Maxwell's equations in a two-constituent composite medium

David J. Bergman; Asaf Farhi

doi:10.1117/12.2246455

3 November 2016 General eigenstates of Maxwell's equations in a two-constituent composite medium

David J. Bergman, Asaf Farhi

Proceedings Volume 10028, Plasmonics II; 100280B (2016) https://doi.org/10.1117/12.2246455
Event: SPIE/COS Photonics Asia, 2016, Beijing, China

Abstract

Eigenstates of Maxwell’s equations in the quasistatic regime were used recently to calculate the response of a Veselago Lens¹ to the field produced by a time dependent point electric charge.^{2, 3} More recently, this approach was extended to calculate the non-quasistatic response of such a lens. This necessitated a calculation of the eigenstates of the full Maxwell equations in a flat slab structure where the electric permittivity ϵ₁ of the slab differs from the electric permittivity ϵ₂ of its surroundings while the magnetic permeability is equal to 1 everywhere.⁴ These eigenstates were used to calculate the response of a Veselago Lens to an oscillating point electric dipole source of electromagnetic (EM) waves. A result of these calculations was that, although images with subwavelength resolution are achievable, as first predicted by John Pendry,⁵ those images appear not at the points predicted by geometric optics. They appear, instead, at points which lie upon the slab surfaces. This is strongly connected to the fact that when ϵ₁/ϵ₂ = −1 a strong singularity occurs in Maxwell’s equations: This value of ϵ₁/ϵ₂ is a mathemetical accumulation point for the EM eigenvalues.⁶ Unfortunately, many physicists are unaware of this crucial mathematical property of Maxwell’s equations. In this article we describe how the non-quasistatic eigenstates of Maxwell’s equations in a composite microstructure can be calculated for general two-constituent microstructures, where both ϵ and μ have different values in the two constituents.

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David J. Bergman and Asaf Farhi "General eigenstates of Maxwell's equations in a two-constituent composite medium", Proc. SPIE 10028, Plasmonics II, 100280B (3 November 2016); https://doi.org/10.1117/12.2246455

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KEYWORDS

Composites

Maxwell's equations

Electromagnetism

Image resolution

Magnetism

Optical spheres

Geometrical optics

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